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Finding Transcendental Numbers?
There are an infinite number of transcendental numbers in (0..1].
Is there a way to find these numbers? If so, is there a way to compute the first 100 digits?
- Someone 5y agoShort answer is that we don’t know well how to find them, but for every one we find we can generate lots of other ones, for example by adding any algebraic number to a known transcendental number (https://en.wikipedia.org/wiki/Transcendental_number#Properties https://en.wikipedia.org/wiki/Transcendental_number#Properti...) If we have a computable number, it is possible to compute its decimal expansion (it might take more time than we want to spend) However, for any sequence of digits, you can find rational, algebraic but not rational, and transcendental numbers starting with it. For example - 123,456/1,000,000 + π/10,000,000 is a transcendental number in (0,1] starting with 0.123456. - 123,456/1,000,000 + √2/10,000,000 is an irrational algebraic number in (0,1] starting with 0.123456. - 123,456/1,000,000 + 1/10,000,000 is a rational number in (0,1] starting with 0.123456